The Modeling Study Of Three Phase Transformer Based On Unified Electrical Quantity Transformation Matrix Method

The establishment of a suitable and accurate three phase transformer model is the basic work of power flow calculation in distribution system,the derivation of the node admittance matrix is the key to the modeling of three phase transformer.At present,the symmetric component method and the incidence matrix method are predominantly used to derive the transformer node admittance matrix.The symmetric component method has a faster speed in program operation,but it is no longer applicable when the three phase parameters of the transformer are asymmetric.The incidence matrix method for transformer whether the parameters of three-phase situation does not require,but when the primary winding or secondary winding of the transformer with ungrounded wye connection,due to the neutral voltage is not zero,the incidence matrix is no longer applicable to express the relationship between branch voltage and node voltage,and the traditional incidence matrix method is no longer applicable.Proposed the unified electrical quantity transformation matrix method.The voltage transformation matrix and the current transformation matrix can be expressed uniformly in the form of block matrix,which solves the problem that the current transformation matrix needs to be calculated according to the connection mode of the transformer during the transformer modeling process.The unified transformation matrix and the basic secondary voltage transformation matrix can be used to derive the secondary voltage transformation matrices of different connection groups,the voltage transformation matrix and the current transformation matrix is further obtained.Improved the problem that the electrical quantity transformation matrix method needs additional transformation to derive the transformer secondary voltage transformation matrix with different secondary winding voltage polarities,which makes the derivation process of the transformer node admittance matrix easier.Proposed the incidence matrix method with neutral parameters.In this method,the neutral point is regarded as a node,the relationship between the transformer branch electrical quantity and the node electrical quantity can be expressed by the incidence matrix containing the neutral point parameters,so the incidence matrix method can be applied to the derivation of the transformer model with ungrounded wye connection.By using this method,the secondary side voltage incidence matrices of all connected groups can be obtained through the transformation matrix and the basic incidence matrix,and then the voltage incidence matrix is obtained.In the three-phase power flow calculation,the three-phase transformer model established by the incidence matrix method with the neutral parameters can incorporate the neutral parameters into the node admittance matrix.This method can not only obtain the transformer neutral voltage conveniently,but also make the transformer model more suitable for power flow calculations with asymmetric three-phase parameters.Because there are many connection groups of three-phase transformers,and the node admittance matrices of different connection groups are also different.It is laborious to derive all connection groups of transformer models by manual derivation,and the accuracy of derivation cannot be guaranteed.By using the MATLAB symbolic operation to design the algorithm,a more intuitive three-phase transformer model can be obtained.It is verified by transformer examples that both methods can obtain results accurately and quickly.In addition,the IEEE-4 node test system is used as an example to verify the correctness of the transformer model contains neutral parameters.